Two-dimensional random walk description of fluid flow in the presence of a wall: The origin of stick versus slip boundary conditions in the continuum limit

H. Dekker and I. Oppenheim

Physica A: Statistical Mechanics and its Applications, 1983, vol. 117, issue 1, 1-16

Abstract: It is shown how a fairly simple random walk on a lattice provides insight into the nature of hydrodynamic boundary conditions. In a flow parallel to the boundary, collisions of up and downward moving particles induce lateral bulk diffusion. At the wall the model accounts essentially for 1) specular reflection, 2) diffuse reflection and 3) trapping at the surface. The steady state is solved exactly. In the continuum limit the case of stick versus slip boundary conditions is explained in its relation to the interplay of bulk and boundary processes.

Date: 1983
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:117:y:1983:i:1:p:1-16

DOI: 10.1016/0378-4371(83)90018-3

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